| Regularity for weakly (K1, K2)-quasiregular mappings |
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| 引用本文： | 高红亚. Regularity for weakly (K1, K2)-quasiregular mappings[J]. 中国科学A辑(英文版), 2003, 46(4) |
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| 作者姓名： | 高红亚 |
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| 作者单位： | College of |
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| 基金项目： | 河北大学校科研和教改项目 |
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| 摘 要： | In this paper, we first give the definition of weakly (K1, K2)-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse Holder inequality, we obtain their regularity property: For any ql that satisfies 0 < K1n(n+4)/22n+1 × 100n2[23n/2(25n + 1)](n - q1) < 1, there exists p1 = p1(n, q1, K1, K2) > n, such that any (K1, K2)-quasiregular mapping f ∈W(loc)(1,q1)(Ω,Rn) is in fact in W(loc)(1,p1)(Ω,Rn). That is, f is (K1, K2)-quasiregular in the usual sense.
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Regularity for weakly (K1, K2)-quasiregular mappings |
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| GAO HongyaCollege of Mathematics and Computer Science,Hebei University,Baoding ,China. Regularity for weakly (K1, K2)-quasiregular mappings[J]. Science in China(Mathematics), 2003, 46(4) |
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| Authors: | GAO HongyaCollege of Mathematics Computer Science Hebei University Baoding China |
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| Affiliation: | College of Mathematics and Computer Science, Hebei University, Baoding 071002, China |
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| Abstract: | In this paper, we first give the definition of weakly (K1,K2)-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse Holder inequality, we obtain their regularity property: For any q1 that satisfies 0＜K1n(n+4)/22n+1×100n2[23n/2(25n+1)](n - q1) ＜ 1, there exists p1 = p1(n,q1,K1,K2)＞n, such that any (K1,K2)-quasiregular mapping f ∈ W1,q1loc(Ω,Rn) is in fact in W1n,p1loc (Ω, Rn). That is, f is (K1, K2)-quasiregular in the usual sense. |
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| Keywords: | weakly (K1 K2)-quasiregular mapping Hodge decomposition weakly reverse Holder inequality regularity. |
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